Some landowners may be denying police access to fields and woods in order to shield illegal hunts from prosecution, animal welfare groups suggested yesterday.

The allegation surfaced as tens of thousands of riders and spectators braved the cold for the first traditional Boxing Day meetings held since hunting with dogs was banned. The Home Office is now coming under pressure to strengthen the Hunting Act, which critics on both sides of the blood sports controversy describe as unenforcable.

More than 250 hunts gathered across the country in high streets, outside public houses and on the lawns of stately homes to demonstrate continued defiance of the law. The Boxing Day turnout this year was one of the largest in memory, the only visible difference being fewer hounds and the presence of birds of prey hired by hunts to exploit a disputed loophole in the legislation.

At least 4,000 supporters assembled near Didmarton, Gloucestershire, to watch the Beaufort Hunt, one of the country's largest. The Prince of Wales, his sons, William and Harry, and the Princess Royal have all ridden with its hounds in the past.

"Everything is pretty much as normal for a Boxing Day meet, but support is up, definitely," said Nigel Maidment, the Beaufort's secretary. "There's a very resilient feeling - people want to see an end to this stupid act."

Among those present was Jim Barrington, former director of the League Against Cruel Sports, who acts as a consultant to the Parliamentary Middle Way group and has called for an end to the ban. He advocates the licensing of hunts.

"A ban is not the right way forward," he said. "My aim is not to target hunters but to improve animal welfare. The Hunting Act is a ridiculous piece of legislation. It is unenforceable and will cause greater animal suffering. Hunting with dogs, whatever you think about it, does not wound [the fox]. It is all or nothing."

In the village of Tarporley hundreds of supporters lined the streets to cheer on the Cheshire Hunt, which was founded in 1762 and is the oldest surviving club. The riders, in red and black tunics, set out accompanied by only two hounds and a European eagle owl.

The local Conservative MP, Stephen O'Brien, addressed the crowd. "In the light of legislation," he said, "hunts are quite rightly looking carefully to ensure they comply with the law and carry on with traditions which exemplify the very highest values within our rural communities."

The assistant chief constable of Sussex, Nigel Yeo, who is the public order spokesman for the Association of Chief Police Officers (Acpo), yesterday called on the Home Office to provide extra powers so that police can monitor what is happening on private land.

"There is no power of entry for police in the [Hunting] act," he told the Times, "though there is a power of entry to seize items connected with hunting. There is not a power of entry to see what is going on ...[Acpo] have made the observation to government that that right is not there and it could be an impediment on occasions."

The League Against Cruel Sports yesterday supported demands for greater powers and claimed that not all landowners were cooperating with the police. "I [have heard] that landowners are refusing police the right to go on their land," Mike Hobday, the League's spokesman, said.

"Surely there are landowners out there who know the law is being broken? I have spoken to police officers who have asked for access to watch and people have said no. We will be talking to ministers about this." The new powers could be included in clauses of the animal welfare bill, currently before parliament, or the next criminal justice bill, he suggested.

The Association of Lawyers for Animal Welfare also backed demands for additional powers. "There is strong anecdotal evidence that some hunts are flouting the law," said David Thomas, one of the organisation's directors. "The police must have the powers to ensure they can enforce it properly, as with any criminal offence ... Some [hunts] appear determined to show they are above the law, which is clearly unacceptable in a democracy".

The Home Office yesterday said it was not aware of any formal request, but a spokeswoman said: "As we normally do in such circumstances, if the police ask us for greater powers to enforce a law we will look at it."

Passage of the Hunting Act provoked fury at Westminster and the government has shown no eagerness for reopening the issue. Downing Street yesterday confirmed it had no plans fresh legislation.

The Countryside Alliance yesterday disputed claims that landowners were obstructing the police. "Landowners and hunts have been working very closely with the police," insisted Jill Grieve, a spokeswoman for the body which led opposition to the Hunting Act. "We are working within the law. There's a good relationship between them all. I don't think there's any obstruction or ill will there."

There have been no convictions of hunt officials or followers since the law came into force last February. A private prosecution, brought by the League Against Cruel Sports against the huntsman of the Exmoor Foxhounds is due to be heard in Barnstaple, Devon, early next year.

FAQ The law and the loopholes

What does the Hunting Act permit? Hunts may use two dogs to flush a fox or other quarry towards someone who will shoot it. Hunts may also deploy a full pack of hounds to follow a scent trail or for exercise.

How have hunts responded to the restrictions? Some hunts have been advised that several pairs of hounds can be used in different parts of the same field in the process of flushing a mammal towards a gun. A number of hunts admit they have had "accidents" when packs of hounds out exercising or trail hunting came across a fox.

Why have some hunts bought eagles? To exploit clauses within the act intended to enable falconry to continue. The government, however, has warned that using a pack of hounds to flush a mammal towards a bird of prey would not give legal cover for a traditional chase.

What is the problem with access to private land? The act permits the police to enter private land to seize items connected with illegal hunting. Officers do not have the automatic right to access merely to watch or monitor a hunt. Animal welfare groups claim that hunting is continuing out of sight and unaffected by the ban.

How many foxes have died since the ban started? Prior to the ban, Defra estimated 100,000 foxes were deliberately killed each year in England and Wales. Of those, four-fifths were shot. The Countryside Alliance maintains the ban will lead to the shooting of many more foxes.